Without using the derivative show that the function `f(x)=7x-3` is strictly increasing function on `R` .

Explanation

To show that the function \( f(x) = 7x - 3 \) is strictly increasing on \( \mathbb{R} \) without using derivatives, we can follow these steps:

### Step 1: Define two points
Let \( x_1 \) and \( x_2 \) be two points in \( \mathbb{R} \) such that \( x_2 > x_1 \). We can express \( x_2 \) in terms of \( x_1 \) and a positive number \( a \) as follows:
\[ x_2 = x_1 + a \quad \text{where } a > 0 \]

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